Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence

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Abstract

In the short note, six proofs for the limit of ratios of consecutive terms in Fibonacci sequence are provided, including using Weierstrass-Bolzano theorem, series method, by definition of limit, difference equation method, matrix method, algebraic method.

Keywords

Ratio , Fibonacci number , limit , golden ratio , Weierstrass-Bolzano theorem , series method , definition of limit , difference equation method , matrix method , algebraic method
  • Chao-Ping Chen Department of Applied Mathematics and Informatics, Jiaozuo Institute of Technology, Jiaozuo city, Henan 454000, China
  • Ai-Qi Liu Sanmenria College of Vocational Technology, Sanmenria City, Henan 472000, China.
  • Feng Qi Department of Applied Mathematics and Informatics, Jiaozuo Institute of Technology, Jiaozuo city, Henan 454000, China
  • Pages: 23–30
  • Date Published: 2003-10-01
  • Vol. 5 No. 3 (2003): CUBO, Matemática Educacional

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Published

2003-10-01

How to Cite

[1]
C.-P. Chen, A.-Q. Liu, and F. Qi, “Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence”, CUBO, vol. 5, no. 3, pp. 23–30, Oct. 2003.

Issue

Vol. 5 No. 3 (2003): CUBO, Matemática Educacional

Section

Articles